Synchronised firing patterns in a random network of adaptive exponential integrate-and-fire neuron model

Acknowledgements This study was possible by partial financial support from the following Brazilian government agencies: CNPq, CAPES, and FAPESP (2011/19296-1 and 2015/07311-7). We also wish thank Newton Fund and COFAP.Peer reviewedPostprin

Statistics of finite-time Lyapunov exponents in the Ulam map

The statistical properties of finite-time Lyapunov exponents at the Ulam point of the logistic map are investigated. The exact analytical expression for the autocorrelation function of one-step Lyapunov exponents is obtained, allowing the calculation of the variance of exponents computed over time intervals of length $n$. The variance anomalously decays as $1/n^2$. The probability density of finite-time exponents noticeably deviates from the Gaussian shape, decaying with exponential tails and presenting $2^{n-1}$ spikes that narrow and accumulate close to the mean value with increasing $n$. The asymptotic expression for this probability distribution function is derived. It provides an adequate smooth approximation to describe numerical histograms built for not too small $n$, where the finiteness of bin size trimmes the sharp peaks.Comment: 6 pages, 4 figures, to appear in Phys. Rev.

Conformational study and reassessment of the vibrational assignments for Norspermidine

The present study presents and discusses the conformational preferences of Norspermidine (NSpd). The effects of varying the dielectric constant on the conformational preferences are discussed, with a view to infer which conformation will correspond to the most stable in the pure condensed liquid phase. Within the same context, a set of NSpd-NH3 molecular adducts were simulated in order to determine the relevance of intermolecular hydrogen bonding on the overall stability and relative positioning of the respective vibrational frequencies. The calculations presently performed allowed a reassessment of the vibrational assignments for NSpd. A full assignment of the NSpd vibrational spectra is presented, with special emphasis being given to the vibrational modes that proved to be most affected by hydrogen bonding. The various inconsistencies of a prior study found in the literature were identified and rectified

Efficiency of free energy calculations of spin lattices by spectral quantum algorithms

Quantum algorithms are well-suited to calculate estimates of the energy spectra for spin lattice systems. These algorithms are based on the efficient calculation of the discrete Fourier components of the density of states. The efficiency of these algorithms in calculating the free energy per spin of general spin lattices to bounded error is examined. We find that the number of Fourier components required to bound the error in the free energy due to the broadening of the density of states scales polynomially with the number of spins in the lattice. However, the precision with which the Fourier components must be calculated is found to be an exponential function of the system size.Comment: 9 pages, 4 figures; corrected typographical and minor mathematical error

Model for tumour growth with treatment by continuous and pulsed chemotherapy

Peer reviewedPreprin

On the Dynamics of Bianchi IX cosmological models

A cosmological description of the universe is proposed in the context of Hamiltonian formulation of a Bianchi IX cosmology minimally coupled to a massless scalar field. The classical and quantum results are studied with special attention to the case of closed Friedmann-Robertson-Walker model.Comment: 11 pages, 1 figur

Complex transitions to synchronization in delay-coupled networks of logistic maps

A network of delay-coupled logistic maps exhibits two different synchronization regimes, depending on the distribution of the coupling delay times. When the delays are homogeneous throughout the network, the network synchronizes to a time-dependent state [Atay et al., Phys. Rev. Lett. 92, 144101 (2004)], which may be periodic or chaotic depending on the delay; when the delays are sufficiently heterogeneous, the synchronization proceeds to a steady-state, which is unstable for the uncoupled map [Masoller and Marti, Phys. Rev. Lett. 94, 134102 (2005)]. Here we characterize the transition from time-dependent to steady-state synchronization as the width of the delay distribution increases. We also compare the two transitions to synchronization as the coupling strength increases. We use transition probabilities calculated via symbolic analysis and ordinal patterns. We find that, as the coupling strength increases, before the onset of steady-state synchronization the network splits into two clusters which are in anti-phase relation with each other. On the other hand, with increasing delay heterogeneity, no cluster formation is seen at the onset of steady-state synchronization; however, a rather complex unsynchronized state is detected, revealed by a diversity of transition probabilities in the network nodes

Anomalous synchronization threshold in coupled logistic maps

We consider regular lattices of coupled chaotic maps. Depending on lattice size, there may exist a window in parameter space where complete synchronization is eventually attained after a transient regime. Close outside this window, an intermittent transition to synchronization occurs. While asymptotic transversal Lyapunov exponents allow to determine the synchronization threshold, the distribution of finite-time Lyapunov exponents, in the vicinity of the critical frontier, is expected to provide relevant information on phenomena such as intermittency. In this work we scrutinize the distribution of finite-time exponents when the local dynamics is ruled by the logistic map $x \mapsto 4x(1-x)$. We obtain a theoretical estimate for the distribution of finite-time exponents, that is markedly non-Gaussian. The existence of correlations, that spoil the central limit approximation, is shown to modify the typical intermittent bursting behavior. The present scenario could apply to a wider class of systems with different local dynamics and coupling schemes.Comment: 6 pages, 6 figure

Validity of numerical trajectories in the synchronization transition of complex systems

We investigate the relationship between the loss of synchronization and the onset of shadowing breakdown {\it via} unstable dimension variability in complex systems. In the neighborhood of the critical transition to strongly non-hyperbolic behavior, the system undergoes on-off intermittency with respect to the synchronization state. There are potentially severe consequences of these facts on the validity of the computer-generated trajectories obtained from dynamical systems whose synchronization manifolds share the same non-hyperbolic properties.Comment: 4 pages, 4 figure